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Fencing problem  

Member rating: 5 out of 10 stars (1 vote) | Words: | Submitted: Wed Aug 27 2003

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Fencing problem I realise intuitively that a circle will cover the largest area, but it is hard to prove it. I decided to do this logically, according to the sheet, by looking at the area that can be covered by a rectangle. I decided to produce a table, and then a graph, showing varying lengths and breadths in a logical manner, decreasing one by 50, and increasing the other by 50. These are my preliminary results: Width (m) 150 175 200 225 250 275 300 325 350 Length (m) 350 325 300 275 250 225 200 175 150 AREA (m2) 52500 56875 60000 61875 62500 61875 60000 56875 52500 I produced a graph showing area from this: You can see that this graph is a parabola, so the highest point will indicate the greatest area, which is 62,500. I have put the base along the x axis because you can work out the other two sides of a rectangle from one side (multiply X2, then you will be left with a number, divide it by two to get the other side). This...

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